Cooperation and profit allocation for two-echelon logistics pickup and delivery problems with state–space–time networks

2021 ◽  
pp. 107528
Author(s):  
Yong Wang ◽  
Shuanglu Zhang ◽  
Xiangyang Guan ◽  
Jianxin Fan ◽  
Haizhong Wang ◽  
...  
Keyword(s):  
State Space ◽  
Space Time ◽  
Pickup And Delivery ◽  
Profit Allocation

scholarly journals Lp-valued stochastic convolution integral driven by Volterra noise

2018 ◽  
Vol 18 (06) ◽  
pp. 1850048 ◽  
Author(s):  
Petr Čoupek ◽  
Bohdan Maslowski ◽  
Martin Ondreját
Keyword(s):  
Banach Space ◽  
State Space ◽  
Stochastic Partial Differential Equations ◽  
Main Tool ◽  
Space Time ◽  
Convolution Integral ◽  
Hölder Continuous ◽  
Stochastic Convolution ◽  
Wiener Chaos ◽  
Convolution Integrals

Space-time regularity of linear stochastic partial differential equations is studied. The solution is defined in the mild sense in the state space [Formula: see text]. The corresponding regularity is obtained by showing that the stochastic convolution integrals are Hölder continuous in a suitable function space. In particular cases, this allows us to show space-time Hölder continuity of the solution. The main tool used is a hypercontractivity result on Banach-space valued random variables in a finite Wiener chaos.

scholarly journals Worldline CPT and massless supermultiplets

2016 ◽  
Vol 31 (27) ◽  
pp. 1650152 ◽  
Author(s):  
Alex S. Arvanitakis ◽  
Luca Mezincescu ◽  
Paul K. Townsend
Keyword(s):  
Quantum Theory ◽  
Minkowski Space ◽  
State Space ◽  
Gauge Invariance ◽  
Massless Particle ◽  
Space Time ◽  
Cpt Invariance ◽  
Minkowski Space Time ◽  
Chern Simons

The action for a massless particle in 4D Minkowski space–time has a worldline-time reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the [Formula: see text]-extended superparticle is shown to be anomalous when [Formula: see text] is odd; in the supertwistor formalism this is because a CPT-violating worldline-Chern–Simons term is needed to preserve the chiral [Formula: see text] gauge invariance. This accords with the fact that no massless [Formula: see text] super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when [Formula: see text] is even, but it has [Formula: see text] states when [Formula: see text] is odd (e.g. the [Formula: see text] hypermultiplet) in contrast to just [Formula: see text] when [Formula: see text] is even (e.g. the [Formula: see text] Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when [Formula: see text] is odd.

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